Practical Considerations

The AA algorithm generates phase profiles, $\Phi^{in}(\vec r)$, that vary continuously between 0 and $2 \pi$. Actually creating a phase element with continuously varying phase delay is difficult; usually only a small number of discrete levels are available. Discretizing the output of the adaptive-additive algorithm necessarily introduces errors. These can be minimized by integrating the discretization step into the AA algorithm itself, as shown in Fig. 3, although this can lead to problems with convergence.